Wednesday, March 17, 2010

Though Logicomix is in no way historically accurate, it portrays well a feeling that I think a lot of us share. I'm sure that a lot of people saw the delicate beauty in Euclid's Elements, in the (relative?) certainty of mathematics, and hoped that something remotely similar to Elements can be made to solve dilemmas that come up in every day life--a consistent philosophical system deduced from the basic facts that everyone would understand and agree upon.

I had the naiive thought once. It's comforting to believe that there's a way to make a limited set of assumptions about life and existence, and derive from those a consistent set of beliefs about everything from metaphysics to ethics to politics.

From what other people are saying around the interweb, I'm not sure if Bertrand Russel would be the right person to attribute this set of feelings to. Actually, this might sound weird, but a more appropriate person would be Ayn Rand.

I recall in Atlas Shrugged, she speaks of people -- even philosophers (and logicians?) -- using logic to prove that logic is flawed/inadequate. These people were, of course, the "bad guys", the people that are held by the masses to be the "leader" of their chosen fields, but who are really there to foil the heros, the proponents of logic.

I loath hearing things about so and so "used logic to prove that logic is inadequate". I heard it once on numb3rs, too, so it's quite annoying. I had no idea that this in fact had been done. It's Gödel's Incompleteness Theorem. Of course!

Did Ayn Rand know about Gödel? Would that changed her mind in any way? If we make the assumptions that (1) human life/experience/society is much more complicated than the natural numbers, and (2) a system of philosophy (built up from a few axioms, for our purpose) can be thought of as a model of the world, then Gödel seems to imply that any of our philosophical system is either incomplete or inconsistent.